Do objects actually shrink?

Are objects that appear relatively smaller from a stationary frame of reference actually smaller for that frame of reference.
Example: If a person were to put their hand 1 inch from a table saw's blade. Then run the saw at such a high rpm that the diameter of the blade appears to shrink down from 10 inches to 1 inch. Then the person moves there hand 2 inches closer to the blade. Will their hand be cut?

Are objects that appear relatively smaller from a stationary frame of reference actually smaller for that frame of reference.
Example: If a person were to put their hand 1 inch from a table saw's blade. Then run the saw at such a high rpm that the diameter of the blade appears to shrink down from 10 inches to 1 inch. Then the person moves there hand 2 inches closer to the blade. Will their hand be cut?

I don't think that was the question. GiTS asked, if we had a circular blade that was spinning at high speed in our reference frame, whether our finger would be able to get closer to the center of the blade without hitting the edge than when it wasn't spinning; this is slightly tricky since it involves acceleration so you can't treat the blade as a rigid object, but this page seems to say we can assume that neither the diameter nor the circumference of a spinning disc change as seen in an inertial reference frame where the center is at rest (this thread suggests the reason is that the there'd be no lorentz contraction in the radial direction, so although the disc would want to contract in the circumferential direction, this would just result in the material 'stretching' in this direction).

But on some other thread, I remember someone posted a good example of a sense in which lorentz contraction has to be seen as "real": suppose you have someone carrying a pole whose rest length is greater than the width of a door, but he runs at the door diagonally while carrying the pole parallel to the door--if he runs fast enough, the length of the pole will shrink enough that it is able to fit through the door.

But if the circular saw is spinning at high speed, its velocity vector is perpendicular to the radius of the saw. Since contraction only occurs in the direction of motion, there would be no diminution of the radius of the saw and so no increase in the distance from your hand.

Staff: Mentor

There's also the classic "paradox" of the barn and the pole. If the pole-vaulter runs fast enough, her pole can fit completely inside the barn, in the barn's reference frame, so that (in the barn's reference frame) the doors at each end can briefly close simultaneously, even though the pole doesn't fit inside the barn when it is at rest.

How can that be possible if the moving pole is not really shorter than the barn, in the barn's reference frame?

Basically, it comes down to your definition of "really", and whether you require that "really" be invariant across different reference frames.

But if the circular saw is spinning at high speed, its velocity vector is perpendicular to the radius of the saw. Since contraction only occurs in the direction of motion, there would be no diminution of the radius of the saw and so no increase in the distance from your hand.

That's apparently correct according to the sources I posted above, but to me it's not so intuitively obvious. Suppose you had a rubber band that was stretched larger than its natural size, but pushed into a circular shape by a bunch of springs arranged like spokes on a wheel, with the rubber band as the tire. Since the rubber band wants to shrink, won't it push down on the springs and thus shrink both the circumference and the radius of the circle until there's an equilibrium in the forces? If so, doesn't it seem intuitively possible something similar could happen in the case of the spinning disc, where the disc "wants" to shrink in the circumferential direction due to Lorentz contraction, even though there is no Lorentz contraction in the radial direction? Is it possible the answer would actually depend somewhat on the physical properties of the disc?

There's also the classic "paradox" of the barn and the pole. If the pole-vaulter runs fast enough, her pole can fit completely inside the barn, in the barn's reference frame, so that (in the barn's reference frame) the doors at each end can briefly close simultaneously, even though the pole doesn't fit inside the barn when it is at rest.

How can that be possible if the moving pole is not really shorter than the barn, in the barn's reference frame?

Basically, it comes down to your definition of "really", and whether you require that "really" be invariant across different reference frames.

"simultaneously" ....from whose point of view? see the complete story here:

Staff: Mentor

so that (in the barn's reference frame) the doors at each end can briefly close simultaneously

"simultaneously" ....from whose point of view?

Ahem...

And no, you cannot see the length contraction in the proper frame.

Quite true. Nothing "really" happens to the pole, in the sense that the runner carrying the pole cannot detect any contraction. Nevertheless, the physical consequences of length contraction are very "real" in the barn's reference frame. We're dealing with two kinds of "realness" here, and everyday language isn't adequate to distinguish between them concisely.

Quite true. Nothing "really" happens to the pole, in the sense that the runner carrying the pole cannot detect any contraction. Nevertheless, the physical consequences of length contraction are very "real" in the barn's reference frame. We're dealing with two kinds of "realness" here, and everyday language isn't adequate to distinguish between them concisely.

True. On both accounts. It is interesting to mention that Lorentz and FitzGerald (to a greater extend) thought that length contraction can be detected in the proper frame. To my best knowledge, FitzGerald went to his grave believing it. Today we know better

But on some other thread, I remember someone posted a good example of a sense in which lorentz contraction has to be seen as "real": suppose you have someone carrying a pole whose rest length is greater than the width of a door, but he runs at the door diagonally while carrying the pole parallel to the door--if he runs fast enough, the length of the pole will shrink enough that it is able to fit through the door.

Presumably you mean the pole is parallel to the door from the door's point of view. I haven't time to think this through in detail, but I think from the pole's point of view, the door shrinks but the pole is at an angle to the door so will still fit through it.

Forget travelling at high speeds for the moment. If my pen is too long to fit in some narrow enclosure, I can simply rotate it and then put it in. Of course we normally use sines and cosines to do rotation in Euclidean space. Well, because of that little minus sign in the metric, we use hyperbolic sines and cosines.

The object doesn't shrink any more than my pen does when I rotate it. All that happens is that projecting the length onto some axis will give a smaller (or larger depending on the rotation and the axis) value.

Lots of relativity problems become exceedingly simple. Thinking about four-vectors easily explains how energy is "rotated" into momentum and so on. I think a lot of this simplicity is obscured in awkward looking Lorentz transformations in introductory relativity texts, but considering I learnt in that order too and will never be able to experience it any other way, I'm not really qualified to comment.

Presumably you mean the pole is parallel to the door from the door's point of view. I haven't time to think this through in detail, but I think from the pole's point of view, the door shrinks but the pole is at an angle to the door so will still fit through it.

Yeah, I was just thinking in terms of the door's rest frame...I think you're right about what would be happening in the pole's rest frame, since the door must shrink in this frame but the pole still has to get through it. Anyway, GiTS' question was just about how "real" Lorentz contraction is in the frame where the object is moving (not the object's own rest frame), so I think this example illustrates a sense in which it has to be seen as real, even though it should not be taken to mean that the pole is "objectively" shorter than the doorway in a frame-independent way.